OK if you have got the pump running, it should run wether its connected to the carbies or not..........I am not sure what the go is with that problem, it sounds a bit strange....
If it was only a light kink, that wouldn't make much difference - if it was *fully* kinked like 90deg or thereabouts, then yes that would stop fuel flow.
You need to get the manual for your bike to dig any deeper into the fuelling problems, hopefully a ZX9 owner will jump on here soon with the answer to your problems........